Needs to use R. Individuals diagnosed with a certain type of cancer are informed

Question

Needs to use R. Individuals diagnosed with a certain type of cancer are informed treatment involves two surgery types: procedure A or procedure B, but not both. Researchers who wish to compare the success rates of these two procedures collect simple random samples of each type of the success rates of these two procedures collect simple random samples of each type of surgery patient and the number of patients with a one year non-recurrent rate is recorded. The data are as follows. Use an alpha = 0.01 error rate to determine if the difference in the two procedures is significant.

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P1 = P2

Alternative hypothesis: P1 P2

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a two-proportion z-test.

Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

p = (p1 * n1 + p2 * n2) / (n1 + n2)

p = 0.55

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

SE = 0.05745

z = (p1 - p2) / SE

z = - 1.044

where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 1.044 or greater than 1.044.

Thus, the P-value = 0.2984

Interpret results. Since the P-value (0.2984) is greater than the significance level (0.01), we have to accept the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that two procedures are signifucantly different.

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.